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Discover the mathematical foundations of quantum mechanics in this newly published book

A book that gives a self-contained treatment of the mathematical foundations of quantum mechanics

World Scientific


IMAGE: The cover of the book pays homage to David Hilbert and John von Neumann, the founding fathers of the mathematical foundations of quantum mechanics. view more

Credit: World Scientific, 2015

Most books about fundamental quantum mechanics use results in the theory of Hilbert space operators without proving them, while most books about Hilbert space operators do not treat quantum mechanics. In addition, they often use fairly advanced results from other branches of mathematics assuming the reader to be already familiar with them, but this is seldom true.

In Franco Gallone's latest book published with World Scientific, "Hilbert Space and Quantum Mechanics" aims to give a really self-contained treatment of all the elements of the theory of Hilbert space operators that are necessary for a sound and mathematically accurate exposition of the principles of quantum mechanics.

This exposition is the object of the final part of the book, where the principles of quantum mechanics are discussed with complete mathematical accuracy and with an unstinting effort to trace them back to the experimental reality that lies at their root. No previous knowledge of quantum mechanics is required. The statistical aspects of quantum mechanics are compared and contrasted with the same aspects of classical physics.

An important characteristic of the book is that the mathematical theory is developed only assuming familiarity with elementary analysis. To make cross-reference as easy as possible, almost every bit of the book is marked with a three numbers code. In all the mathematical proofs, logical deduction is thoroughly assisted with this system of cross-reference.

All the proofs are written in minute detail; in them, however, previous results are always quoted by just their three numbers codes, without spelling them out; this enables experts to pursue the logic of a proof without too many diversions, and beginners to receive all the support they might need.

The book is of interest to researchers and graduate students in functional analysis, who can see how closely an important part of their chosen field is linked with quantum mechanics, and also to physicists, who can see how the abstract language of functional analysis brings unity to the apparent distinct approaches employed in quantum theory.


This book is sold in major bookstores at US$138 / £91. More information on the book can be found at

About World Scientific Publishing

World Scientific Publishing is a leading independent publisher of books and journals for the scholarly, research and professional communities. The company publishes about 500 books annually and more than 120 journals in various fields. World Scientific collaborates with prestigious organisations like the Nobel Foundation, US National Academies Press, as well as its subsidiary, the Imperial College Press, amongst others, to bring high quality academic and professional content to researchers and academics worldwide. To find out more about World Scientific, please visit

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